Spintronic leaky-integrate-fire spiking neurons with self-reset and winner-takes-all for neuromorphic computing

Neuromorphic computing using nonvolatile memories is expected to tackle the memory wall and energy efficiency bottleneck in the von Neumann system and to mitigate the stagnation of Moore’s law. However, an ideal artificial neuron possessing bio-inspired behaviors as exemplified by the requisite leaky-integrate-fire and self-reset (LIFT) functionalities within a single device is still lacking. Here, we report a new type of spiking neuron with LIFT characteristics by manipulating the magnetic domain wall motion in a synthetic antiferromagnetic (SAF) heterostructure. We validate the mechanism of Joule heating modulated competition between the Ruderman–Kittel–Kasuya–Yosida interaction and the built-in field in the SAF device, enabling it with a firing rate up to 17 MHz and energy consumption of 486 fJ/spike. A spiking neuron circuit is implemented with a latency of 170 ps and power consumption of 90.99 μW. Moreover, the winner-takes-all is executed with a current ratio >104 between activated and inhibited neurons. We further establish a two-layer spiking neural network based on the developed spintronic LIFT neurons. The architecture achieves 88.5% accuracy on the handwritten digit database benchmark. Our studies corroborate the circuit compatibility of the spintronic neurons and their great potential in the field of intelligent devices and neuromorphic computing.

Magnetic field driven DW motion dynamics in patterned devices with SAF structure. a Major and minor K-H loops of the patterned device. Hex refers to effective field from RKKY interaction. b Kerr images of the device recorded under a combined interlayer exchange coupling field Hex and a constant external Hz field. c DW position as a function of time during integrate, leaky and falling processes. Pink regions depict the DW integrate process at effective OOP field Hz+HRKKY = -87. 5 Oe and the blue regions refer to DW leaky and falling processes at effective OOP field Hz+HRKKY = 66.5 Oe. Kerr images illustrate the corresponding domain configuration in a timeframe. Upper histogram shows the DW velocity during the integrate, leaky and falling processes.
Parallelly, the results of realizing the LIF characteristics of neurons by driving DW motion with equivalent effective magnetic fields are shown in Supporting Information Figure S1. A series of strip devices were fabricated to investigate the dynamic processes of DW rising and falling. A constant negative B-field was applied and the DW was found to move rightward under an effective field of -87. 5 Oe including the stray field and external field, emulating the process of rising. Subsequently, during the falling procession, the external field was reduced and the DW began to move to the left at 66.5 Oe effective field. The complete motion process of DW is shown in the Supporting Information Figure S1b-c with the corresponding Kerr images and DW velocity at the different moments as illustrated in the insets and the bar chart, respectively.

Note S1
To alleviate the DW motion stochasticity issue in the present work, the synergistic cooptimization approach was employed via engineering device fabrication process and tailoring LIFT neuron devices' operation mechanism.
 Device fabrication process optimization: The film surface/interface disorder and the roughness of device edge can be improved by optimizing the film deposition technology and device fabrication process [1][2][3][4] . In our work, besides securing the high-quality epitaxial growth of the films stack with post annealing treatment to reduce the intrinsic disorders and pinning effectively, the dedicated devices fabrication processes (i.e., the improved lithography with Al hard-mask and the optimized ion-beam etching with 30 o tilting angle and rotation) were systematically executed to reduce the edge roughness and to minimize the imperfection sites, as verified by below tabulated extensive scanning electron microscopy (SEM) and atomic force microscopy (AFM) scanning images data with illustration of improved side-wall topology and edge roughness. Figure S2. Typical SEM and AFM images data with the illustration of improved side-wall topology, morphology, and edge roughness, after devices fabrication engineering by using Al hard-mask (HM) and tilted ion-beam etching (IBE) process optimization.
 Device mechanism and working principle: Importantly, based on our device's working mechanism, the temperature increase caused by Joule heating is the inducement of DW motion, and the relationship between the pinning barrier and temperature satisfies the Kurkijärvi model [i.e., , the temperature dependence of the depinning field per S4 reports 5,6 , and the pinning field decreases with increasing temperature simultaneously. This allows domain walls to maintain consistent magnetization structures during propagation, fundamentally plays important role in harnessing the DW motion stochasticity issue, in turn facilitating the SNN implementation with competitive digit recognition accuracy and performance.
Upon synergistic co-optimization with the maximized effective field acting on the DW, so that the DW motion falls closer to the flow regime. As shown in Figure S3, the phenomenon of stochastic DW motion has been significantly improved. Figure S3. Extensive observation of dynamic DW motion emulated LIFT processes upon synergistic co-optimization with a maximized effective field acting on the DW, complementarily facilitating our established spintronic LIFT neuron model for spiking neural network implementation.

Note S2
The extensive experiments of RKKY effective field extraction were performed as a function of the current with 25 repetitions on each single data point. The field induced by non-Joule-heatinginduced-field (current-induced field, CIF) can be calculated by the modulated RKKY effective field at different positive and negative currents using the following equations, Figure S4. The dependence and contribution of the effective field induced by current polarity.
Therefore, we calculated CIF and plotted the relationship between CIF and current amplitude, as shown in Figure S4. The dependence of the effective field polarity on the current shows an approximate linear relationship, about 1.34 Oe/mA, which is quite limited in our experiment. As manifested in the Figure 3b, with less than 5 Oe the non-Joule-heating-induced rider field strength is <10% portion of JHIF. Clearly, as depicted in Figure 3b, the JHIF is dominated in modulation of the RKKY interaction, corroborated by our reproducible experiments.  Figure S6 Schematic model of Joule Heat modulated RKKY interaction in the tailored SAF heterostructure.

Supporting Information
As specifically elaborated in the Supporting Information Figure S6, a schematic model of Joule heating modulated RKKY interaction is discussed in detail with insights into the DW motion dynamics. By modulating the thickness of the spacer layer in the stacked structure samples prepared in our experiments, the films with different RKKY coupling strength can be adjusted precisely. In our samples, the strong FM coupling between perpendicularly spin-polarized CoFeB and Co leads to a coherent magnetization switching. When the field is swept from the negative saturation to the positive saturation, the CoFeB and Co ferro-coupled magnetization switches synchronously first due to the strong RKKY interaction. When the external field is large enough, the Co/Pt multilayer also switches, and finally the hysteresis loop presents a triple loop as shown in Figure 1f in the main text.
Based on our experimental results and simulation studies, the plausible mechanism of DW motion driven by competition between the intrinsic built-in field (i.e., stray field) and RKKY field in the thin films stack is discussed in detail. In the micron-scale device in our experiment, the internal S9 stray field is much smaller than the RKKY field and can be negligible 7,8 . Correspondingly, a relatively weak external magnetic field is applied with opposite polarity to RKKY field. As a result, the effective field subjected to DW in CoFeB and Co layers is positive, which can drive the down-up DW to move to the left, emulating the neuron leaky process. When the device is manipulated by the Joule heating generated via a pulsed current flow, the RKKY coupling decreases linearly with increasing temperature. Consequently, the amplitude of RKKY effective field is smaller than the external Hz field, and the net effective field is negative, leading to DW moving rightward and mimicking the characteristics of neuron integrate in a biological manner. However, when the device is shrink to nanoscale size, the strong stray field inside the SAF film 8 with opposite polarity plays a critical role in competing the RKKY field, elaborating the same functions as micro-scale samples.
The Joule heating induced RKKY modulation is ascribed to the following mechanisms 9 :

Spacer contribution
The interlayer-exchange-coupling is reduced due to the softening of the Fermi edge at higher temperature.

Interface contribution
The complex reflection coefficients at the spacer/magnet interface is highly energy dependent, which results in a strong dependence on temperature.

Magnetic layers
Collective excitation within the magnetic layers will reduce the free energy of the system. The overall influence of the above factors on RKKY interaction can be written as: Approximately, within a certain temperature range, the following relationship is derived as follows: The basic dynamic process of DWs and corresponding simulation parameters are shown in Supporting Information Figure S7 and Table S2, respectively.

Note S3
To comprehensively demonstrate the performance of the device, we have listed the calculations of power and energy consumption of our device and the data extracted from other highly relevant reports.  Table S4.

MTJ Model
The parallel resistance of MTJ can be expressed by Brinkman model 16  , where RA is the resistance-area product.
When in a fully antiparallel state, the resistance of MTJ is described by the following equation 16 : where TMR is the tunneling magnetoresistance ratio.
As a result, the resistance of MTJ can be expressed as: where MTJ x is the location of the center of MTJ and MTJ l is the length of MTJ.

Mathematic model of DW motion:
The process of DW falling is nonlinear with position due to the dynamic RKKY interaction.
Therefore, a polynomial scheme involves only non-negative integer powers or only positive integer exponents of a variable is applied to fit the results of micromagnetic simulations to obtain the specific expression of DW velocity as function of the time and the position.